A synthesizer is an electronic instrument capable of imitating the sound of many traditional instruments, and of producing unique musical sounds of its own.
The concept has a long history. The traditional pipe organ has numerous sets of pipes controlled with stops, producing a variety of different tone colors. Some have names like "flute," "strings," "trombone," and even "Vox humana" (human voice).
The word "synthesizer" derives from the concept of synthesizing a complex waveform out of simple ones, particularly sine waves. Fourier analysis consists of breaking a complex waveform into sine waves, so the converse process is called synthesis. The 1934 Hammond Organ used this technique, producing sine waves with stable and precise tuning by an electromagnetic system known as tonewheels. However, even though it was using additive synthesis, it was not called a "synthesizer."
The 1955 RCA Music Synthesizer was the first machine to receive the name. It was a room-sized machine using vacuum tubes. It was controlled by a prepunched paper tape, like a player piano. It had no keyboard or any means for a musician to "play" it. The music laboriously prepared for it was played in strict rhythm. RCA released a few recordings produced by this device, but it was never more than a curiosity. Nevertheless, it was able not only to produce different timbres and tone colorations, but vibrato, and instrument-like attacks and decays. It really does sound rather like a modern "synthesizer."
By the late 1960s and 1970s, solid-state electronics made analog synthesizers more inexpensive and practical, and Robert Moog in particular developed a series of synthesizers which had keyboards as interfaces and began to attract the attention of musicians. A breakthrough occurred in 1968 when Walter Carlos released Switched-on Bach, an LP of Bach piece which he "realized" on a specially-built Moog synthesizer. These synthesizers were still not performance instruments; they could only play one part at a time, and Carlos had to assemble his pieces on a multitrack recorder. The genuinely musical quality of his "realizations" took the synthesizer out of the realm of a novelty or a source of sound effects (like the Theremin) and touched off a wave of synthesizer use.
By the 1990s, digital electronics made it possible for synthesizers to be performance instruments, playing chords and supplying effect such as vibrato in real time. Improved synthesis algorithms and the use of "sampled" sounds recorded from real instruments made it possible for synthesizers to produce not only electronic sounds but extremely convincing imitations of traditional instrument sounds. In performances of works such as musical comedies and operettas, a sole synthesizer player could produce a tolerable rendition of the score all by himself; not as good as a real 15-piece pit band, of course, but far better than a pianist playing a "piano reduction" of the score.
The synthetic transformation can be the result of any of several processes, including the subtraction of qualities from a sound, the addition of qualities to a sound, modulation of pitch, waveform, and sound phase, and also from digitally-sampled sounds.